Identifying critical operations of a production process

ABSTRACT

Identifying an operation that is critical to meeting a due date of a production order includes identifying operations associated with the production order, obtaining schedules for the operations using infinite production planning, obtaining start intervals for the operations based on the schedules, selecting a target operation from the operations, and determining whether the target operation is critical to meeting the due date based on whether the target operation can be scheduled, using finite production planning, in a start interval obtained for the target operation.

CLAIM TO PRIORITY

This patent application claims priority to German Patent ApplicationDE102005006608.9, filed on Feb. 11, 2005, the contents of which arehereby incorporated by reference into this application as if set forthherein in full.

TECHNICAL FIELD

This patent application relates generally to identifying an operation ofa production process that is critical to meeting a due date of aproduction order.

BACKGROUND

Producers today face volatile markets, decreasing customer commitments,mass production, and shorter product life cycles. In response, producershave turned to flexible production planning and supply chain management(SCM).

Generally speaking, SCM encompasses cross-company coordination andoptimization of material, information, and value within a value creationchain. One goal of SCM is to provide customers with products atagreed-upon due dates at relatively low cost. This goal can be achievedif production planning enables producers to plan delivery due datesrelatively precisely. Different factors, however, may impact the abilityto plan delivery due dates precisely. For example, different operationsmay be required to satisfy a production order. These operations maydepend on the availability of different resources, and it may bedifficult to ascertain the availability of those resources.

As noted above, production processes may include different operations,examples of which include, but are not limited to, processing steps,transportation of products between locations, manufacturing intermediateproducts, and assembling intermediate products into end products.Different operations can depend on each other, creating a network ofdependencies. In order to provide production planning in such anenvironment, SCM includes enterprise resource planning (ERP) software,which provides planning and optimizing tools. One example of suchsoftware, the Advanced Planner and Optimizer (APO) from SAP® AG,facilitates planning and detailed scheduling of operations needed tosatisfy productions orders. APO may use data from demand planning andsupply network planning utilities in order to plan operations based onavailability of resources.

Production planning software such as APO, however, is not currentlyconfigured to identify critical operations of a production process. A“critical” operation, in this context, is an operation that acts as abottleneck or an interruption in the production process if it is notperformed according to specific parameters (e.g., at a specific time).As a result, production planners need to examine production processesmanually in order to determine which operation(s) are critical tomeeting the due date of a production order.

SUMMARY

This application features methods, systems, and apparatus, includingcomputer program products, for identifying an operation of a productionprocess that is critical to meeting a due date of a production order.Aspects thereof are set forth below.

In general, in one aspect, the invention is directed to identifying anoperation that is critical to meeting a due date of a production order.This aspect includes identifying operations associated with theproduction order, obtaining schedules for the operations using infiniteproduction planning, obtaining start intervals for the operations basedon the schedules, selecting a target operation from the operations, anddetermining whether the target operation is critical to meeting the duedate based on whether the target operation can be scheduled, usingfinite production planning, in a start interval obtained for the targetoperation. Other aspects may include one or more of the followingfeatures.

The foregoing aspect may include scheduling an operation that occursafter the target operation using infinite production planning.Determining whether the target operation is critical to meeting the duedate may include determining whether the production order meets the duedate. Obtaining the schedules may include backward scheduling theoperations from the due date to obtain latest start times for theoperations, and/or forward scheduling the operations from a predefinedtime to obtain earliest start times for the operations. Obtaining thestart intervals may include, for each operation, comparing an earlieststart time to a latest start time.

Infinite production planning may include scheduling operations withouttaking availability of resources into account. Finite productionplanning may include scheduling operations while taking availability ofresources into account.

The foregoing aspect may include selecting a second target operationfrom the operations, and determining whether the second target operationis critical to meeting the due date. The foregoing aspect may includeincreasing times for operations other than the target operation toobtain a reduced start interval for the target operation. Determiningwhether the target operation is critical may include determining if thetarget operation can be scheduled in the reduced start interval. Theforegoing aspect may include selecting at least one other operation, anddetermining if the at least one other operation can be scheduled in astart interval for the at least one other operation.

The foregoing aspect may include increasing the times of the operationsafter determining whether the target operation is critical, andcontinuing to increase the times of the operations until the startinterval reaches a predetermined threshold. The foregoing aspect mayinclude specifying a threshold value for use in identifying a criticaloperation. The threshold value may be used in determining whether thetarget operation is critical.

The target operation may be determined to be non-critical if the targetoperation can be scheduled in the start interval. The target operationmay be determined to be critical if the target operation cannot bescheduled in the start interval.

The details of one or more examples are set forth in the accompanyingdrawings and the description below. Further features, aspects, andadvantages of the invention will become apparent from the description,the drawings, and the claims.

DESCRIPTION OF THE DRAWINGS

FIG. 1A is a graph depicting infinite production planning.

FIG. 1B is a graph depicting infinite production planning with sequenceplanning.

FIG. 2 is a graph depicting finite production planning.

FIG. 3 a flowchart of a process for detecting a lead-time problem in aninfinite production planning process.

FIG. 4A is a graph depicting production planning with a lead-timeproblem.

FIG. 4B is a graph depicting production planning with a critical path.

FIG. 5 a flowchart of a process for detecting critical operations inproduction.

FIG. 6A is a graph depicting production planning using two productionorders and three operations for a production order.

FIG. 6B is a graph depicting production planning with start intervals.

FIG. 6C is a graph depicting production planning that uses infiniteproduction planning to detect a critical operation in production.

FIG. 6D is a graph depicting production planning with shortened startintervals.

FIG. 6E is a graph depicting production that uses finite productionplanning to detect a critical operation.

FIG. 7 a flowchart of a process for determining a shortened startinterval and for detecting critical operations in production.

FIG. 8 a flowchart of a process for determining a shortened startinterval, for detecting a negative start interval, and for detectingcritical operations in production.

Like reference numerals denote like elements in the figures.

DETAILED DESCRIPTION

In order to ensure customer satisfaction, production orders must befilled on time. Production orders can be characterized by the operationsthat they necessitate, and by the time that those operations require tosatisfy the production orders. During automated production planning,multiple production orders can be accepted. Processes needed to satisfythese production orders should be scheduled so that the orders aresatisfied on time. Because different production orders may require thesame resources, certain resources may be over-committed. For example, iftwo operations attempt to access the same resource, the capacity of theresource may not be sufficient to perform both operations at the sametime. One operation can take precedence at the expense of the otheroperation. The capacity of a resource can thus be one possibleconstraint during production planning. Examples of other types ofconstraints are described in the following.

Generally speaking, assigning a resource to an operation requires thatthe resource be also available at a particular time. Only if enough ofthe resource is available, can an operation be planned for thatresource. For example, machines have certain operational times and downtimes. These times dictate when a resource may have machine access.Thus, operations can be assigned a resource at fixed times, which maynot change.

Resources can be divided into blocks. Blocks may include time slots inwhich a resource can only produce products with certain characteristics.An operation can only be planned within such a block if the operation isto produce such a product.

Resources may be linked. For example, an end point of a first resourcecan initiate a starting point of second resource. Waiting times betweenthese, or any other, resources may be defined. For example, there may beminimum and maximum waiting times.

Oftentimes, machines need to be supplied with specific tools needed tomanufacture a certain product. Incorporating the tools into the machinemay take time. This so-called “tooling-time” may need to be taken intoaccount during production planning. Tooling-times may be different fordifferent successions of operations.

The foregoing are but a few constraints considered in productionplanning processes. Additional constraints also may be considered, ifapplicable.

There are different types of production planning processes currently inuse. Among these are finite production planning and infinite productionplanning.

In infinite production planning, resources are planned for allproduction orders without considering whether the resources required tosatisfy those production orders are available, or whether other timingconstraints are met. For example, if two operations require the sameresource at the same time, this information is not taken into accountduring infinite production planning. By contrast, finite productionplanning takes into account capacity and availability of resources whenscheduling resources for a production order. Finite production planningcan thus be used to determine whether a production plan is executable.However, as explained in more detail below, finite production planningdoes not identify critical operations of a production process.

FIG. 1A illustrates a production plan implemented using infiniteproduction planning. Four different resources A, B, C, and D are shown.Use of resources A to D by operations 2, 4, 6, 8, 10, 12, 16 is depictedalong a time axis. Each block represents one operation. The length of ablock represents the duration of the corresponding operation. Operations2, 4 are for a first production order. Operations 6, 8, 10, 12 and 16are for a second production order. A due date 14 for the secondproduction order is also shown.

As shown in FIG. 1A, resource A is used by operation 2. At the end ofoperation 2, operation 10 also uses resource A. There is an overlap timeduring which both operations 2 and 10 use resource A. Resource B is usedby both operations 12 and 16. Operations 12 and 16 overlap on resourceB. Resource C is used by operation 4. At the end of operation 4, thereis an overlap time during which both operations 4 and 8 use resource C.Resource D is used by operation 6.

Because the production plan of FIG. 1A is generated by infiniteproduction planning, it is not possible to determine whether operationscan be performed on a resource. More specifically, in infiniteproduction planning, no checks are performed to determine if twooperations use the same resource at the same time.

FIG. 1B shows an infinite production planning process that take intoaccount a sequence of operations associated with one production order.Thus, operation 8 may only start after operation 6 is finished, andoperation 12 may only start after operations 8 and 10 are finished.However, operations 2 and 10, and 4 and 8, may overlap.

In finite production planning, it is possible to determine whether aresource is available for a particular operation, and to schedule theresource accordingly. Finite production planning thus provides aproduction plan that is actually executable. However, the duration of aproduction plan created by finite production planning is not optimized.Several operations could be rescheduled to obtain shorter deliverytimes, however, it is not possible to automatically determine whichoperations which can be rescheduled.

During finite production planning, it is checked whether a resource isavailable. There can be various constraints that may limit availabilityof the resource. One constraint may be the capacity of the resource.Capacity constraints can be that all plans, part lists, and intermediateproducts need to be available, consistent, and complete for production.All necessary tools may also need to be available, along with personnelwith any required qualifications. One disadvantage of finite productionplanning is that it may schedule production so that an a productionorder is satisfied after its agreed-upon due date.

FIG. 2 illustrates a production plan implemented using finite productionplanning. Resource A is used by operation 2 first. Only after performingoperation 2 can resource A be used by operation 10. Resource C is usedby operation 4, and can only be used by operation 8 after operation 4 isperformed. Resource B is used first by operation 12 and then byoperation 16. Because operation 16 is the last operation in a productionorder, and it is finished after due date 14, this production order isnot satisfied on time.

Thus, to provide efficient production planning, to reduce lead-times, toincrease throughput of products, and to reduce inventory cost,production planning needs to take into account capacity of resources.However, as explained above, finite production planning may lead toproduction orders that are not satisfied on time. With infiniteproduction planning, on-time schedules can be obtained. But, thoseschedules are unrealistic due to physical limitations of the resourcesinvolved.

FIG. 3 shows an infinite production planning process for use indetecting whether there is a lead-time problem, meaning whether there isinsufficient time in a schedule to satisfy a production order. Process21 plans (22) operations of a production order using infinite productionplanning backwards, starting from the date that the production order isdue, i.e., the due date. After planning, process 21 determines (24) ifone operation in the resulting schedule is before the current time(i.e., in the past). If no operation is in the past, then there is nolead-time problem (34). Backward infinite production planning of theoperations permits identification of the latest start point for each ofthe operation. The latest start point is the latest point in time atwhich an operation can be started and still meet the production orderdue date. These latest start points are stored in memory.

If the latest start time of one operation is in the past, there is alead-time problem (26) with the schedule. The lead time problem meansthat more time is required, than is available, to finish all operationsin sequence in order to satisfy the production order.

When a lead-time problem occurs, process 21 schedules (28) alloperations using infinite production planning from the current time(start point) forward (meaning into the future). With “forward” infiniteproduction planning, earliest start points of operations can beidentified. The earliest start point is the point in time at which anoperation can begin after start of production. The earliest start pointsare stored in memory.

Process 21 determines, for each operation, whether the earliest startpoints are different from the latest start points. If the earliest andlatest start points for an operation are different, then the operationis considered to be flexible in terms scheduling. Shifting the starttimes of operations such as these may not affect the due date.

Process 21 designates (30) all operations with fixed start points (i.e.,the same earliest and latest dates) as being on a critical path of theproduction order. Shifting (32) the termination of one or moreoperations on a critical path may resolve the lead-time problems sothat, in the end, the production order is satisfied (34) on time.

FIG. 4A illustrates a lead-time problem graphically. In FIG. 4A,operations 6, 8, 10, 12 are scheduled using infinite production planningwith sequence planning. As shown in FIG. 4A, operation 12 is finishedafter due date 14. This means that the lead-time of the production orderis longer than the time available to satisfy the production order.Process 21 may be used to identify operations that are critical in termsof the lead-time.

More specifically, after scheduling operations 6, 8, 10, 12 backwardsfrom due date 14 with infinite production planning, the start time ofoperation 6 dictates a starting point 20, as shown in FIG. 4B. From thestarting point 20, all operations are planned forward using infiniteproduction planning. This enables identification of the earliest startpoints for operations 6, 8, 10, 12. As shown in FIG. 4B, the earliestand latest start points of operation 10 differ. (Operation 10 isillustrated as solid block when started at its latest start point and asa dotted block when started at its earliest start point.) All otheroperations 6, 8, 12 cannot be shifted and have fixed start points.Therefore, these operations constitute the critical path. Changes in theschedule of operations that are on the critical path have a directaffect on the time that it will take to satisfy the production order, asnoted above.

However, identifying lead-time problems and resolving those problemsonly on critical paths does not take into account capacity problems ofresources A to D. In this regard, changes on the critical paths may leadto overlaps with other production orders on resources A to D. Also,shortening durations of operations on critical paths might not lead tosatisfying the production order earlier, since some operations that arenot on the critical paths may be constrained to start only after acapacity problem with a resource has been resolved. Such a problem onsuch a resource may lead to a delay in satisfying the production ordereven though the operation was not on the critical path. For this reason,identifying critical paths in a finite production plan might not resultin identification of operations that are, in fact, responsible fordelays in satisfying the production order.

FIG. 5 shows a process 41 for identifying critical operations takinginfinite and finite production planning into account. From a startingpoint, which may be the current time, process 41 schedules (40)operations of a production order using forward infinite productionplanning. The earliest start points of the operations are identifiedfrom the resulting schedule, and stored. Also, starting from the duedate, process 41 schedules (42) operations of the production order usingbackward infinite production planning. The latest start points of theoperations are identified from the resulting schedule, and stored.

After identifying the earliest start times and the latest start times ofthe operations, process 41 identifies (44) a start interval each of theoperations. The start interval is the time between the earliest starttime and the latest start time of an operation.

FIG. 6A shows two production orders, which include three operations 2,4, 6 and 8, 10, 12. In FIG. 6A, there are capacity constraints on eachof the resources A, B, and C. Operation 12 can only be started afteroperation 6 is finished due to limited capacity on resource C. Operation10 can only be started after operation 4 is finished due to limitedcapacity on resource B. Operation 8 can only be started after operation2 is finished due to limited capacity on resource A. Thus, the scheduleof FIG. 6A does not meet due date 14.

FIG. 6B illustrates the same operations as in FIG. 6A. First, operations12, 10, 8 are scheduled using forward infinite production planningstarting from start point 20. This results in the dotted blocks foroperations 8, 10, 12. As a result, the earliest possible start points ofoperations 8, 10, 12 can be identified from FIG. 6B. Then, operations 8,10, 12 are scheduled using backward infinite production planningbeginning at due date 14. This results in the solid blocks foroperations 8, 10, 12. As a result, the latest possible start points ofoperations 8, 10, 12 can be identified from FIG. 6B

For each operation, the time interval between the earliest start timeand the latest start time is the start interval. For operation 8, thisis start interval 9; for operation 10, this is start interval 11; andfor operation 12, this is start interval 13. These start intervals areobtained without taking into account resource capacityproblems/limitations.

Returning to FIG. 5, after process 41 identifies (44) start intervals 9,11, 13, process 44 designates one operation to be the target operation.For this target operation, process 41 executes (48) finite productionplanning starting from the operation's start point. Process 41determines (50) whether, with finite production planning, the targetoperation can be started within a previously determined start interval.If not, the target operation is identified as critical. Otherwise, thetarget operation is identified as non-critical.

Process 41 determines (52) if the number of critical operations meets(or exceeds) a predetermined threshold. If so, process 41 does notdesignate any further target operations. If not, process 41 designates(56) another target operation and proceeds as described above withrespect to the newly-designated target operation.

FIG. 6C illustrates, graphically, a process for determining whether,using finite production planning, target operations can be started intheir corresponding start intervals. As shown, operation 12 can bestarted in its start interval 13. Operation 10 can also be started inits start interval 11. Operation 8 cannot be started within its startinterval 9. Thus, operation 8 is identified as critical.

However, identifying operations that can be started in their respectivestart intervals may not necessarily make these operations non-critical.For example, two operations that result in delay of the production ordercan be critical even though both of those operations can be startedwithin their corresponding start intervals.

FIG. 7 shows a process 61 for identifying critical operations that canbe started in their corresponding start intervals. Process 61 may beused to supplement processes 21 and/or 41, or it may be usedindependently thereof. During process 61, only operations that have notyet been deemed critical using the processes described above areanalyzed. To identify operations as critical, the start interval of eachsuch operations is shortened.

Process 61 selects (60) one operation to be the target operation.Process 61 schedules (62) all other (non-target) operations forward andbackward using infinite production planning. During this scheduling(62), the durations of all operations are increased so that they arelonger than actually necessary. These increases result in a new startinterval for the target operation. Specifically, because the durationsof the non-target operations increase, the start interval of the targetoperation decreases.

Process 61 schedules the target operation using finite productionplanning and determines (64) whether the target operation can be startedin the shortened start interval. If the target operation cannot bestarted in the shortened start interval, the target operation is deemedcritical (66). If the target operation can be started in the shortenedstart interval, the target operation is not necessarily deemed (68)critical or non-critical. Process 61 determines (70) whether thepredetermined threshold value has been reached. If the threshold valuehas been reached (72), process 61 terminates. Otherwise, process 61returns (74) the start intervals to their original durations, selects(60) another operation, and designates the selected operation as thetarget operation.

In the foregoing manner, each of the operations may be selected anddesignated as the target operation. After all operations have beenselected as target operations and checked for criticality, the durationof all operations is increased and the operations are again selected astarget operations, and the foregoing checking process is repeated. Thisprocess is performed until a threshold value of critical operations isobtained.

FIG. 6D illustrates identifying critical operations using shortenedstart intervals. In FIG. 6D, operation 12 is selected and is designatedas the target operation. After increasing the duration of operation 10,the earliest and latest start times of operations 10, 12 are obtained.This results in a shortened start interval 13 for operation 12.Operation 12 is scheduled using finite forward planning. It is thendetermined whether operation 12 can be started in the shortened startinterval 13. In this case, operation 12 can be started in the shortenedstart interval 13, as shown in FIG. 6D.

Operation 10 is selected as the next target interval. After increasingthe duration of operation 12, the earliest and latest start times ofoperations 10, 12 are determined. This results in a shortened startinterval 11 for operation 10. After scheduling using finite productionplanning, as per FIG. 6E, it is checked, whether operation 10 can bestarted in the shortened start interval 11. As shown in FIG. 6E,operation 10 cannot be started in interval 11. Accordingly, operation 10is deemed critical.

Should the start interval becomes negative, e.g., because of a changedduration of the operations, the earliest start point can be after thelatest start point. In this case, a point in time (as opposed to aninterval of time) is obtained that is between the earliest start pointand the latest start point after changing the duration of theoperations. FIG. 8 shows a process for doing this. The process of FIG.8, namely process 81, may be used to supplement processes 21 and/or 41or may be used independently thereof. In this regard, the blocks of FIG.8 that are similar to those of FIG. 7 are not described here.

FIG. 8 illustrates reduction of a start interval to a start point. Afteridentifying the earliest and latest start points with a changedduration, the target operation (62) is checked to determine (80) whetherthe start interval is negative. If the start interval is negative, apoint in time in between the previous interval boundaries is selected.After selection (82), or if the start interval is not negative, thetarget operation is scheduled (84) with finite production planning atthe beginning of the interval. If an operation can be scheduled withfinite production planning at that point in time (which was determinedby the increased duration of the other operations), such an operation isdesignated non-critical.

The processes described herein (“the processes”) are not limited to usewith any particular hardware and software; they may find applicabilityin any computing or processing environment and with any type of machinethat is capable of running machine-readable instructions. All or part ofthe processes can be implemented in digital electronic circuitry, or incomputer hardware, firmware, software, or in combinations thereof.

All or part of the processes can be implemented as a computer programproduct, i.e., a computer program tangibly embodied in an informationcarrier, e.g., in a machine-readable storage device or in a propagatedsignal, for execution by, or to control the operation of, dataprocessing apparatus, e.g., a programmable processor, a computer, ormultiple computers. A computer program can be written in any form ofprogramming language, including compiled or interpreted languages, andit can be deployed in any form, including as a stand-alone program or asa module, component, subroutine, or other unit suitable for use in acomputing environment. A computer program can be deployed to be executedon one computer or on multiple computers at one site or distributedacross multiple sites and interconnected by a communication network.

Method steps associated with the processes can be performed by one ormore programmable processors executing one or more computer programs toperform the functions of the processes. The method steps can also beperformed by, and the processes can be implemented as, special purposelogic circuitry, e.g., an FPGA (field programmable gate array) and/or anASIC (application-specific integrated circuit).

Processors suitable for the execution of a computer program include, byway of example, both general and special purpose microprocessors, andany one or more processors of any kind of digital computer. Generally, aprocessor will receive instructions and data from a read-only storagearea or a random access storage area or both. Elements of a computerinclude a processor for executing instructions and one or more storagearea devices for storing instructions and data. Generally, a computerwill also include, or be operatively coupled to receive data from, ortransfer data to, or both, one or more mass storage devices for storingdata, e.g., magnetic, magneto-optical disks, or optical disks.Information carriers suitable for embodying computer programinstructions and data include all forms of non-volatile storage area,including by way of example, semiconductor storage area devices, e.g.,EPROM, EEPROM, and flash storage area devices; magnetic disks, e.g.,internal hard disks or removable disks; magneto-optical disks; andCD-ROM and DVD-ROM disks.

All or part of the processes can be implemented in a computing systemthat includes a back-end component, e.g., as a data server, or thatincludes a middleware component, e.g., an application server, or thatincludes a front-end component, e.g., a client computer having agraphical user interface, or any combination of such back-end,middleware, or front-end components. The components of the system can beinterconnected by any form or medium of digital data communication,e.g., a communication network. Examples of communication networksinclude a LAN and a WAN, e.g., the Internet.

Method steps associated with the processes can be rearranged and/or oneor more such steps can be omitted to achieve the same, or similar,results to those described herein.

Elements of different embodiments described herein may be combined toform other embodiments not specifically set forth above. Otherembodiments not specifically described herein are also within the scopeof the following claims.

1. A method of identifying an operation that is critical to meeting adue date of a production order, the method comprising: identifyingoperations associated with the production order; obtaining schedules forthe operations using infinite production planning; obtaining startintervals for the operations based on the schedules; selecting a targetoperation from the operations; and determining whether the targetoperation is critical to meeting the due date based on whether thetarget operation can be scheduled, using finite production planning, ina start interval obtained for the target operation.
 2. The method ofclaim 1, further comprising: scheduling an operation that occurs afterthe target operation using infinite production planning; whereindetermining whether the target operation is critical to meeting the duedate further comprises determining whether the production order meetsthe due date.
 3. The method of claim 1, further comprising: selecting asecond target operation from the operations; and determining whether thesecond target operation is critical to meeting the due date.
 4. Themethod of claim 1, wherein obtaining the schedules comprises backwardscheduling the operations from the due date to obtain latest start timesfor the operations.
 5. The method of claim 4, wherein obtaining theschedules comprises forward scheduling the operations from a predefinedtime to obtain earliest start times for the operations.
 6. The method ofclaim 1, wherein obtaining the start intervals comprises, for eachoperation, comprises comparing an earliest start time to a latest starttime.
 7. The method of claim 1, wherein infinite production planningcomprises scheduling operations without taking availability of resourcesinto account.
 8. The method of claim 1, wherein finite productionplanning comprises scheduling operations while taking availability ofresources into account.
 9. The method of claim 1, further comprisingincreasing times for operations other than the target operation toobtain a reduced start interval for the target operation.
 10. The methodof claim 9, wherein determining whether the target operation is criticalcomprises determining if the target operation can be scheduled in thereduced start interval.
 11. The method of claim 1, further comprising:selecting at least one other operation; and determining if the at leastone other operation can be scheduled in a start interval for the atleast one other operation.
 12. The method of claim 1, further comprisingincreasing the times of the operations after determining whether thetarget operation is critical.
 13. The method of claim 12, furthercomprising continuing to increase the times of the operations until thestart interval reaches a predetermined threshold.
 14. The method ofclaim 1, wherein the target operation is determined to be non-criticalif the target operation can be scheduled in the start interval.
 15. Themethod of claim 1, wherein the target operation is determined to becritical if the target operation cannot be scheduled in the startinterval.
 16. The method of claim 1, further comprising: specifying athreshold value for use in identifying a critical operation; wherein thethreshold value is used in determining whether the target operation iscritical.
 17. A computer program product tangibly embodied in aninformation carrier for identifying an operation that is critical tomeeting a due date of a production order, the computer program productcomprising instructions that cause a machine to: identify operationsassociated with the production order; obtain schedules for theoperations using infinite production planning; obtain start intervalsfor the operations based on the schedules; select a target operationfrom the operations; and determine whether the target operation iscritical to meeting the due date based on whether the target operationcan be scheduled, using finite production planning, in a start intervalobtained for the target operation.
 18. The computer program product ofclaim 17, further comprising instructions that cause the machine to:schedule an operation that occurs after the target operation usinginfinite production planning; wherein determining whether the targetoperation is critical to meeting the due date further comprisesdetermining whether the production order meets the due date.
 19. Thecomputer program product of claim 17, further comprising instructionsthat cause the machine to: select a second target operation from theoperations; and determine whether the second target operation iscritical to meeting the due date.
 20. A system comprising: memory thatstores executable instructions to for use in identifying an operationthat is critical to meeting a due date of a production order; and one ormore processing devices that execute the executable instructions to:identify operations associated with the production order; obtainschedules for the operations using infinite production planning; obtainstart intervals for the operations based on the schedules; select atarget operation from the operations; and determine whether the targetoperation is critical to meeting the due date based on whether thetarget operation can be scheduled, using finite production planning, ina start interval obtained for the target operation.